Class and rank of differential modules

By L. Avramov, R. Buchweitz, S. Iyengar. 2006

50 citations recorded by the source corpus.

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class – a substitute for the length of a free complex – and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c83485efddb4a1d9e4f97447e67970cf5e16fa1d